details

property	value
status	complete
benchmark	Ex1_Luc04b.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.46359 seconds
cpu usage	3.44736
user time	3.24784
system time	0.19952
max virtual memory	1.8407092E7
max residence set size	219468.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given CSR could be proven: (0) CSR (1) CSRRRRProof [EQUIVALENT, 68 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 0 ms] (4) CSR (5) CSRRRRProof [EQUIVALENT, 9 ms] (6) CSR (7) CSRRRRProof [EQUIVALENT, 0 ms] (8) CSR (9) RisEmptyProof [EQUIVALENT, 0 ms] (10) YES ---------------------------------------- (0) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: nats -> cons(0, incr(nats)) pairs -> cons(0, incr(odds)) odds -> incr(pairs) incr(cons(X, XS)) -> cons(s(X), incr(XS)) head(cons(X, XS)) -> X tail(cons(X, XS)) -> XS The replacement map contains the following entries: nats: empty set cons: {1} 0: empty set incr: {1} pairs: empty set odds: empty set s: {1} head: {1} tail: {1} ---------------------------------------- (1) CSRRRRProof (EQUIVALENT) The following CSR is given: Context-sensitive rewrite system: The TRS R consists of the following rules: nats -> cons(0, incr(nats)) pairs -> cons(0, incr(odds)) odds -> incr(pairs) incr(cons(X, XS)) -> cons(s(X), incr(XS)) head(cons(X, XS)) -> X tail(cons(X, XS)) -> XS The replacement map contains the following entries: nats: empty set cons: {1} 0: empty set incr: {1} pairs: empty set odds: empty set s: {1} head: {1} tail: {1} Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(cons(x_1, x_2)) = x_1 + x_2 POL(head(x_1)) = 1 + x_1 POL(incr(x_1)) = x_1 POL(nats) = 0 POL(odds) = 0 POL(pairs) = 0 POL(s(x_1)) = x_1 POL(tail(x_1)) = x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: head(cons(X, XS)) -> X ---------------------------------------- (2) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: nats -> cons(0, incr(nats)) pairs -> cons(0, incr(odds)) odds -> incr(pairs) incr(cons(X, XS)) -> cons(s(X), incr(XS)) popout

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job log

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actions

all output return to TRS Contextsensitive